Method for optimizing reservoir operation for multiple objectives based on graph convolutional neural network and NSGA-II algorithm

ABSTRACT

A method for optimizing a reservoir operation for multiple objectives based on a GCN and a NSGA-II algorithm. The method includes collecting relevant data for reservoir flood-control operation and establishing a multi-objective optimization model for the flood control. An initial population is obtained. Grouping individuals by an encoding operation and the grouped classifications are nodes of the GCN, and mapping parent-child relationships obtained by crossover and mutation operations as edges between the nodes in the GCN. A preliminary Pareto frontier is obtained, abscissas of the preliminary Pareto frontier are grouped and labeled, and a GCN model is trained by using the grouping labels and the graphic structure obtained in Step 2. The nodes in the graphic structure are classified by using the trained GCN model, and a uniformity of the Pareto frontier is adjusted. A set of non-inferior schemes of the multi-objective optimization problem for the reservoir operation is output.

RELATED APPLICATIONS

The present application is a U.S. National Phase of InternationalApplication Number PCT/CN2021/125239 filed Oct. 21, 2021 and claimspriority to Chinese Application Number 202110275101.X filed Mar. 15,2021.

TECHNICAL FIELD

The present disclosure belongs to the field of a multi-objectiveoptimization for a reservoir operation in the water conservancyindustry, and relates to a method for optimizing a reservoir operationfor multiple objectives based on a graph convolutional neural networkand a NSGA-II algorithm.

BACKGROUND

During flood seasons, comprehensive factors such as the dam level of thereservoir and the safety in the downstream need to be taken intoconsideration for the reservoir operation. If only one objectivelowering the water level in the reservoir is considered, it may resultin low environmental efficiencies. Therefore, it is necessary toconsider multiple objectives to adjust the discharge volume at eachstage to obtain a solution set that can make the environmentalefficiencies and flood-control efficiencies non-inferior. Users selectthe operation scheme as required. Whereas in the previous researches,traditional methods, such as a particle swarm algorithm and a geneticalgorithm and dynamic programming method, are commonly adopted to solvethe operation scheme, in which problems such as a dimensional disasterand a slow convergence speed commonly occur when the model is complex.Using the GCN NSGA-II (Non-Dominated Sorting Genetic Algorithm)algorithm to search the Pareto frontier can be used in themulti-objective optimization model for the flood control to search thePareto frontier in the model.

The NSGA-II algorithm is a multi-objective optimization algorithm basedon a Pareto non-inferior solution, which inherits a global searchingability of the traditional genetic algorithms, and has an elite strategyand a fast non-dominated sorting, and therefore, the algorithm has anexcellent effect in rapidly searching the Pareto frontier andmaintaining the population diversity. Whereas in real life, many data donot have a regular spatial structure, the graph neural network can modelthe data in non-Euclidean spaces by using the particularity of thegraphic structure, and capturing the internal dependencies of data hasgreat advantages in mining the node characteristics in the graph.

The patent application (CN110428099A) discloses a method for optimizingan agricultural operation line and an urban water supply capacity basedon a particle swarm algorithm, which obtains a maximum water supplycapacity that meets the requirements on a certain double guarantee rateof agricultural irrigation water and urban water, and solves the problemthat the prior art cannot deal with the multi-objective andmulti-guarantee rate. However, the particle swarm algorithm is prone tolosing the diversity of the population in the searching spaces, therebybeing stuck in the problem of local minimum and being not capable ofguaranteeing the global searching. The patent application (CN109948847A)discloses a multi-objective evolutionary algorithm applied to areservoir group operation. The disclosure improves the fact in thetraditional third-generation non-dominated sorting genetic algorithm(NSGA-III) that the parent population is randomly selected forreproduction by performing two rounds of tournament selections and avector angle selection, and provides a multi-objective evolutionaryalgorithm (VA-NSGA-III) based on a reference point and a vector angleselection. Nevertheless, due to the method provided by this patent, theselection operation during population evolution becomes morecomplicated, which also increases the computational complexity; and isnot conducive to improving the convergence speed of the Pareto frontier.

SUMMARY

The objectives of the present disclosure are to eliminate the defects ofthe prior art and to provide a method for optimizing a reservoiroperation for multiple objectives based on a graph convolutional neuralnetwork and a NSGA-II algorithm. The present disclosure is applied to amulti-objective reservoir optimization operation, which can rapidlyprovide a set of reservoir optimization operation schemes that satisfiesall objectives, thereby facilitating the decision makers to select anoptimal scheme.

In order to solve the above technical problems, the following technicalsolutions are adopted in the present disclosure.

Provided in the present disclosure is a method for optimizing areservoir operation for multiple objective based on a graphconvolutional neural network and a NSGA-II algorithm. The methodincludes the following steps.

In Step 1, relevant data for reservoir flood-control operation arecollected and a multi-objective optimization model for the reservoiroperation is established.

In Step 2, an initial population of a multi-objective optimizationproblem for the reservoir operation is obtained by using the NSGA-IIalgorithm, individuals in the population are grouped by an encodingoperation and the individuals are marked with classifications, each ofwhich is taken as a node in a GCN graphic structure, and parent-childrelationships obtained by crossover and mutation operations are mappedas edges between the nodes in the GCN graphic structure, to obtain theGCN graphic structure and a preliminary Pareto frontier.

In Step 3, abscissas of the preliminary Pareto frontier obtained in Step2 are grouped and labeled, and then a GCN model is trained by using thegrouping labels and the GCN graphic structure obtained in Step 2.

In Step 4, the nodes in the GCN graphic structure are classified byusing the trained GCN model, and then a uniformity of the Paretofrontier is adjusted by using the NSGA-II algorithm until an algorithmiteration ends, to obtain a more uniform Pareto frontier.

In Step 5, according to the more uniform Pareto frontier obtained inStep 4, a set of non-inferior schemes of the multi-objectiveoptimization problem for the reservoir operation is output.

Furthermore, objectives considered in the multi-objective optimizationmodel for the reservoir operation in Step 1 include as follows.

Firstly, an upstream water level is minimized and it is ensured that thereservoir maintains a low water level during a flood season, so as toeffectively ensure safety of a dam. Secondly, a maximum discharge volumein the reservoir is minimized, and the reservoir stores as muchfloodwater as possible to ensure safety in a downstream to minimize aninundation loss.

Moreover, a process of Step 2 specifically includes as follows.

In Step 2.1, the population of the multi-objective optimization problemfor the reservoir operation is randomly initialized, the individuals ofthe populations are encoded according to a following encoding method,and the encoded individual classifications are taken as the nodes in theGCN graphic structure; through the encoding method, a plurality ofindividuals in the population belong to the same classificationrepresented by the same node, to avoid a redundancy in the graphicstructure caused by too many individuals in the population.

The encoding method is that: a definition domain of the maximumdischarge volume Qmax is divided at an equal distance, then eachdistance is ┌Q_(max)/N┐, and then the individuals are encoded by using amethod ┌Q/┌Q_(max)/N┐┐, where Qmax is the maximum discharge volume, N isa number of classifications, that is, a number of nodes in the GCNgraphic structure; the Pareto frontier is divided at an equal distanceaccording to the abscissas, intervals of which are defined as 0, 1, 2 .. . , where a node 0 is defined as an elimination node, and a length ofa gene sequence in the population is determined by a number ofvariables.

In Step 2.2, the crossover and mutation operations are performed on theindividuals in the population in Step 2.1 to determine whether theconstraint conditions are satisfied, and codes in the gene sequence ofeliminated individuals that satisfy the constraint conditions arepointed to the node 0; the individuals that satisfy the conditions arerecorded, and at the same time the parent-child relationships generatedby the crossover and mutation operations are defined as the edges of thegraphic structure.

In addition, a process of Step 3 specifically includes as follows.

In Step 3.1, the preliminary Pareto frontier obtained by the NSGA-IIalgorithm is grouped and labeled according to the abscissas, that is, avalue domain of an objective function is divided at an equal distance,to define digital labels.

In Step 3.2, input parameters are set, relationships between theindividuals in the population are represented as an adjacency matrixA∈R^(N×N) in the graph convolutional neural network, and acharacteristic matrix X∈R^(N×D) is initialized.

In Step 3.3, an input layer with N individuals is taken as a firstportion, that is, an N-layered input layer is constituted by N nodes inthe graph, and the characteristic matrix X and the adjacency matrix Aare taken as inputs.

In Step 3.4, a convolutional layer composed of two layers of graphconvolutions is taken as a second portion, and characteristics of a baselayer are transmitted to a next layer by trigging informationtransmission of the edges between the two layers.

In Step 3.5, an output layer is taken as a third portion, for thecharacteristic matrix X obtained by calculating and transmitting of thetwo layers of the convolutional layers, a classification probability ateach of the nodes is output through an activation function.

Additionally, a process of Step 4 specifically includes as follows.

In Step 4.1, the preliminary Pareto frontier is obtained by the NSGA-IIalgorithm through selection, crossover and mutation operations, duringthis process, relationships of a parent-child tree-shaped structure isgenerated between the individuals in the population of themulti-objective optimization problem for the reservoir operation and thetree-shaped structure is converted into the GCN graphic structure.

In Step 4.2, whether a population iteration threshold being satisfied isdetermined, if so, the GCN is started to be trained, nodecharacteristics in a population evolution relationship graphic networkare learned, and a node classification result is made correspond to aclassification of the Pareto frontier.

In Step 4.3, the nodes are classified by using the GCN, and then theindividuals in the Pareto frontier are adjusted through a loop iterationby using the NSGA-II algorithm, which specifically includes followingsteps.

In Step 4.3.1, the nodes are classified by using the GCN, and thepreliminary Pareto frontier is supplemented and improved.

In Step 4.3.2, the nodes with different classifications in the Paretofrontier are traversed, redundant nodes with the same classification aredeleted, the population of the classifications with a fewer number isincreased to increase differences.

In Step 4.3.3, crossover and mutation operations are performed on thenodes with a good performance obtained through the GCN classification byusing the NSGA-II algorithm to obtain new nodes.

In Step 4.3.4, whether the nodes satisfy the constraint conditions isdetermined, and if so, the nodes are retained.

Compared with the prior art, the present disclosure has the followingadvantages and beneficial effects.

1. In the present disclosure, for the multi-objective optimizationproblem of the reservoir during flood seasons, two objectives of thelowest dam level and the minimum discharge flow are considered, and thesafety of the reservoir and the ecological health problem in thedownstream are taken into account, which are also the main objectives ofthe multi-objective optimization problem of the reservoir operationduring flood seasons. Due to the conflict between these two objectives,and the fact that it needs to consider a series of constraint conditionsfor the problem, it cannot be simply tackled as a single-objectiveproblem. The NSGA-II algorithm has been always used to tackle themulti-objective optimization problem and has been widely used. Theadvantages of the NSGA-II algorithm, such as the fast convergence andstrong global searching ability at the early stage of the algorithm, areinherited by the algorithm provided in the present disclosure, whichalso enables the algorithm in the present disclosure to have a goodeffect in tackling the multi-objective optimization problem of thereservoir operation during flood seasons to obtain a satisfactory Paretosolution set.

2. In the present disclosure, a graph convolutional neural network isintroduced, in which the parent-child relationships between individualsgenerated in the population evolution process of the multi-objectiveoptimization problem are transformed into nodes of the GCN graphicstructure through encoding operations so as to train the GCN model. Thegraph convolutional neural network can well mine the relationshipsbetween the nodes in the graphic structure, and learn the nodecharacteristics, thereby accurately performing the classification, andthereby improving the problems of poor local searching and slowconvergence speed in the NSGA-II algorithm. At the later stage of theNSGA-II algorithm, GCN classification is used in the algorithm providedby the present disclosure, instead of using the strategies, such ascalculating the crowding distance, of the NSGA-II algorithm, to achievethe objectives of reducing computational costs and improving speed.Eventually, the NSGA-II algorithm is used to optimize and adjust the GCNclassification results to obtain an improved Pareto frontier, whichensures the uniformity of the Pareto frontier. In the presentdisclosure, a set of reservoir optimization operation schemes duringflood seasons that satisfies all objectives can be rapidly provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a flow chart of a method for optimizing a reservoiroperation for multiple objectives based on a graph convolutional neuralnetwork and a NSGA-II algorithm according to an embodiment of thepresent disclosure.

FIG. 2 illustrates a gene code and a pareto classification of GCNclassification results in an individual relationship graphic networkaccording to an embodiment of the present disclosure.

FIG. 3 illustrates a structural diagram of a graph convolutional neuralnetwork, including an input layer, a convolutional layer, and an outputlayer according to an embodiment of the present disclosure.

FIG. 4 illustrates a schematic diagram of a node-informationtransmission rule in a graphic structure according to an embodiment ofthe present disclosure.

FIG. 5 illustrates a comparison diagram of Pareto frontiers obtained bythree algorithms according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present disclosure is a method for optimizing a reservoir operationfor multiple objectives based on a graph convolutional neural networkand a NSGA-II algorithm, which optimizes the discharge volume of thereservoir during each time period, and obtains a set of non-inferiorschemes of the multi-objective optimization problem for the reservoiroperation. Relevant data for reservoir flood-control operation arecollected and a multi-objective optimization model for the reservoiroperation is established. An initial population of the multi-objectiveoptimization problem for the reservoir operation is obtained by usingthe NSGA-II algorithm. Individuals in the population are grouped by anencoding operation and the individuals are labeled with classifications,each of which serves as a node in a GCN graphic structure, andparent-child relationships obtained by crossover and mutation operationsare mapped as edges between the nodes in the GCN graphic structure, toobtain the GCN graphic structure and a preliminary Pareto frontier.Abscissas of the obtained preliminary Pareto frontier are grouped andlabeled, and then a GCN model is trained by using the grouping labelsand the obtained GCN graphic structure. The nodes in the GCN graphicstructure are classified by using the trained GCN model, then theuniformity of the Pareto frontier is adjusted by using the NSGA-IIalgorithm until the algorithm iteration ends, and a more uniform Paretofrontier is obtained. A set of non-inferior schemes of themulti-objective optimization problem for the reservoir operation isoutput according to the Pareto frontier adjusted by using the NSGA-IIalgorithm.

Provided in the present disclosure is a method for optimizing areservoir operation for multiple objectives based on a graphconvolutional neural network and a NSGA-II algorithm. The methodincludes the following steps.

In Step 1, relevant data for reservoir flood-control operation arecollected and a multi-objective optimization model for the reservoiroperation is established.

In Step 2, an initial population of a multi-objective optimizationproblem for the reservoir operation is obtained by using the NSGA-IIalgorithm, individuals in the population are grouped by an encodingoperation and the individuals are labeled with classifications, each ofwhich serves as a node in a GCN graphic structure, and parent-childrelationships obtained by crossover and mutation operations are mappedas edges between the nodes in the GCN graphic structure, to obtain theGCN graphic structure and a preliminary Pareto frontier.

In Step 3, abscissas of the preliminary Pareto frontier obtained in Step2 are grouped and labeled, and then a GCN model is trained by using thegrouping labels and the GCN graphic structure obtained in Step 2.

In Step 4, the nodes in the GCN graphic structure are classified byusing the trained GCN model, then a uniformity of the Pareto frontier isadjusted by using the NSGA-II algorithm until an algorithm iterationends, and a more uniform Pareto frontier is obtained.

In Step 5, according to the more uniform Pareto frontier obtained inStep 4, a set of non-inferior schemes of the multi-objectiveoptimization problem for the reservoir operation is output.

Objectives considered in the multi-objective optimization model for thereservoir operation in Step 1 include the followings. Firstly, anupstream water level is minimized to ensure that the reservoir maintainsa low water level during a flood season, thereby effectively ensuringthe safety of a dam. Secondly, a maximum discharge flow in the reservoiris minimized, and the reservoir stores as much floodwater as possible toensure safety in the downstream to minimize an inundation loss.

Step 2 specifically includes the followings.

In Step 2.1, the population of the multi-objective optimization problemfor the reservoir operation is randomly initialized. The individuals inthe population are encoded according to a following encoding method, andencoded individual classifications are taken as the nodes in the GCNgraphic structure. Through the encoding method, a plurality ofindividuals in the population belong to the same classification and arerepresented by the same node, to avoid a redundancy in the graphicstructure caused by too many individuals in the population.

The encoding method is that: a definition domain of the maximumdischarge flow Qmax is divided at an equal distance, then each distanceis ┌Q_(max)/N┐, where Qmax is the maximum discharge volume, and N is anumber of classifications, that is, a number of nodes in the GCN graphicstructure. The individuals are encoded by using a method┌Q/┌Q_(max)/N┐┐. The Pareto frontier is divided at an equal distance bythe abscissas, intervals of which are defined as 0, 1, 2 . . . , where anode 0 is defined as an elimination node, and a length of a genesequence in the population is determined by a number of variables.

In Step 2.2, the crossover and mutation operations are performed on theindividuals in the population in Step 2.1 to determine whether theconstraint conditions are satisfied, and codes in the gene sequence ofeliminated individuals that satisfy the constraint conditions arepointed to the node 0. The individuals that satisfy the conditions arerecorded, and at the same time the parent-child relationships generatedby the crossover and mutation operations are defined as the edges of thegraphic structure.

Step 3 specifically includes the followings.

In Step 3.1, the preliminary Pareto frontier obtained by the NSGA-IIalgorithm is grouped and labelled according to the abscissas, that is, avalue domain of an objective function is divided at an equal distance,to define digital labels.

In Step 3.2, input parameters are set. Relationships between theindividuals in the population are represented as an adjacency matrixA∈R^(N×N) in the graph convolutional neural network, and acharacteristic matrix X∈R^(N×D) is initialized.

In Step 3.3, an input layer with N individuals is taken as a firstportion, that is, an N-layered input layer is constituted by N nodes inthe graph. The characteristic matrix X and the adjacency matrix A aretaken as inputs.

In Step 3.4, a convolutional layer composed of two layers of graphconvolutions is taken as a second portion, and characteristics of a baselayer are transmitted to a next layer by triggering informationtransmission of the edges between the two layers.

In Step 3.5, an output layer is taken as a third portion, for thecharacteristic matrix X obtained by calculating and transmitting of thetwo layers of the convolutional layers, a classification probability ofeach of the nodes is output through an activation function.

Step 4 specifically includes the followings.

In Step 4.1, the preliminary Pareto frontier is obtained by the NSGA-IIalgorithm through selection, crossover and mutation operations. Duringthis process, relationships of a parent-child tree-shaped structure aregenerated between the individuals in the population of themulti-objective optimization problem for the reservoir operation, andthe tree-shaped structure is converted into the GCN graphic structure.

In Step 4.2, whether a population iteration threshold is satisfied isdetermined. If so, it starts to train the GCN, to learn nodecharacteristics in a population evolution relationship graphic network,and to make a node classification result corresponding to aclassification of the Pareto frontier.

In Step 4.3, the nodes are classified by using the GCN, and then theindividuals in the Pareto frontier are adjusted through a loop iterationby using the NSGA-II algorithm, which specifically includes followingsteps.

In Step 4.3.1, the nodes are classified by using the GCN, and thepreliminary Pareto frontier is supplemented and improved.

In Step 4.3.2, the nodes with different classifications in the Paretofrontier are traversed, redundant nodes with the same classification aredeleted, and the population of the classifications with a fewer numberis increased to increase differences.

In Step 4.3.3, crossover and mutation operations are performed on thenodes with a good performance obtained through the GCN classification byusing the NSGA-II algorithm to obtain new nodes.

In Step 4.3.4, whether the nodes satisfy the constraint conditions isdetermined, and if so, the nodes are retained.

The present disclosure will be further described in detail below inconjunction with the accompanying drawings.

FIG. 1 illustrates a flow chart of a method for optimizing a reservoiroperation for multiple objectives based on a graph convolutional neuralnetwork and a NSGA-II algorithm according to an embodiment of thepresent disclosure. FIG. 2 illustrates a gene code and a paretoclassification of GCN classification results in an individualrelationship graphic network according to an embodiment of the presentdisclosure. FIG. 3 illustrates a structural diagram of a graphconvolutional neural network including an input layer, a convolutionallayer, and an output layer according to an embodiment of the presentdisclosure. As illustrated in FIGS. 2 and 3 , the method for optimizingthe reservoir operation for the multiple objectives based on the graphconvolutional neural network and the NSGA-II algorithm provided by thepresent disclosure is applied to the multi-objective optimal problem ofthe flood-control operation in the Xiaolangdi Reservoir to obtain thePareto frontier of the multi-objective optimization problem.

As illustrated in FIG. 1 , the method according to the embodiments ofthe present disclosure includes the following steps.

In Step 1, data such as a storage capacity, a maximum dischargecapacity, a water inflow during a flood season and a natural waterrequirement in the Xiaolangdi Reservoir are collected to establish amulti-objective optimal model for flood-control operation, whichincludes the followings.

In 1.1, the data such as the storage capacity, the maximum dischargecapacity, the water inflow during the flood season and the natural waterrequirement in the reservoir are collected, which are specifically asfollows.

Xiaolangdi Hydro Project is located on the main stream of the YellowRiver 40 km north of Luoyang City, Henan Province, the upstream of whichis Sanmenxia Hydro Project, and the downstream of which is HuayuankouReservoir in Zhengzhou. The dam site controls a watershed area of6940000 km² that accounts for 95.1% of the watershed area beforeHuayuankou. The construction objectives of the Xiaolangdi reservoir aremainly to prevent floods and reduce siltation, while taking into accountof water supply, irrigation and power generation. A designed normalwater storage level is 275 m (Yellow Sea elevation), a check flood levelfor one time occurrence in ten thousand years is 275 m and a designedflood level for one time occurrence in one thousand years is 274 m. Atotal designed storage capacity is 12.65 billion m³, including 7.55billion m³ for a sediment storage capacity, 4.05 billion m³ for aflood-control storage capacity, and 1.05 billion m³ for a storagecapacity for water and sediment operation. The highest level forflood-control operation is 275.0 m and the corresponding storagecapacity is 9.422 billion m³.

In 1.2, the multi-objective optimal model for the flood-controloperation is established.

In 1.2.1, the lowest dam level is MinF₁=Min{MaxZ_(t)}, where Z_(t)represents the dam level during the t-th time period.

In 1.2.2, the minimum of the maximum discharge flow isMinF₂=Min{MaxQ_(t)}, where Q_(t) represents the discharge flow of thereservoir during the t-th time period in the operation period.

In 1.2.3, the constraint conditions are as follows.

1. A dam level constraint is Z_(t,min)(230 m)<Z_(t)<Z_(t,max) (275 m)where Z_(t,min) and Z_(t,max) represent a minimum and maximum waterlevel constraint during the t-th time period in the reservoir operationperiod, respectively; and Z_(t) is the dam level of the reservoir duringthe t-th time period.

2. A reservoir balance constraint is V_(t)=V_(t-1)+(I_(t)−Q_(t))Δt,where V_(t) represents the storage capacity of the reservoir during thet-th time period; and I_(t) and Q_(t) represent the inflow and dischargeflow of the reservoir during the t-th time period, respectively.

3. A discharge capacity constraint is Q≤Q_(max)(14900 m³/s), whereQ_(max) represents a maximum discharge capacity of the reservoir underthe corresponding water level.

In Step 2, the graphic structure of the graph convolutional neuralnetwork (GCN) is established by reproducing the offspring through theNSGA-II algorithm.

In Step 2.1, the number of individuals in the population is randomlyinitialized to 50, and the population is encoded according to a certainencoding method, as illustrated in FIG. 2 .

The range of the discharge volume is divided at an equal distance, andthen each distance is ┌Q_(max)/N┐, where Q_(max) represents the maximumdischarge volume, and N is the number of classifications. Theindividuals are encoded in the manner of ┌Q/┌Q_(max)/N┐┐, and N isselected as 26, that is, it is divided into 26 classifications, i.e.,the first classification is Qt∈[0, 573]. It is set to satisfy that thealgebraic threshold is 40. The Pareto frontier is to be divided at anequal distance length of 0.00016 by the abscissas if excess of 40generations, The 0 node is initialized as the elimination node, and [1,2, 3, 4] are the classifications on the Pareto frontier, respectively.These five nodes of 0 to 4 become the source nodes, and the length ofthe gene sequence in the population is determined as 72 by the number ofvariables.

In Step 2.2, the crossover and mutation operations are performed on theindividuals in the population to determine whether the constraintconditions are satisfied. Codes in the gene sequence of eliminatedindividuals that satisfy the constraint conditions are pointed to thenode 0. The individuals that satisfy the conditions are recorded, and atthe same time, the results of crossover and mutation, that is, theindividual relationships of the parent-child relationships, arerecorded.

In Step 2.3, according to the population obtained by the NSGA-IIalgorithm the parent-child tree-shaped structure is converted into thegraphic structure, that is, the population evolution relationshipgraphic network G, required by the GCN.

In Step 3, the relationships between the nodes are mined through theGCN, and the characteristics of the nodes are continuously enriched totrain the GCN, as illustrated in FIG. 3 .

In Step 3.1, input parameters are set, relationships between theindividuals in the population are represented as an adjacency matrix Ain the graph convolutional neural network, and a specific characteristicmatrix X is determined by the reachable lengths of the paths in thegraph.

In Step 3.2, an input layer with 50 individuals is taken as a firstlayer, that is, 50 nodes and 5 source nodes, i.e. 55 nodes, in the graphform the input layer, and the above-mentioned characteristic matrix andthe adjacency matrix A serve as inputs.

In Step 3.3, a convolutional layer composed of two layers of graphconvolutions is taken as a second layer, and the transmission betweenthe two layers is based on the following transfer rules:

${{f( {H^{(1)},A} )} = {\sigma( {{\hat{D}}^{- \frac{1}{2}}\hat{A}{\hat{D}}^{- \frac{1}{2}}H^{(1)}W^{(1)}} )}},$where characteristics of this layer are transmitted to a next layer bytriggering the information transmission of the edges, as illustrated inFIG. 4 .

In Step 3.4, the last layer is the output layer. The characteristicmatrix Z, that is, the classification probability of each node, obtainedby the calculation and the transmission of the above-mentioned twolayers of the convolutional layers is output through the functionsoftmax.

In Step 4, the GCN nodes are classified, and the nodes with goodclassification results continue to be reproduced through NSGA-II toadjust the performance of the nodes.

In Step 4.1, through the evolution processes (crossover, mutation andelimination) of individuals in the NSGA-II genetic algorithm, theevolution processes of the individuals are modelled into a populationrelationship network graph.

In Step 4.2, whether the population iteration threshold (the thresholdis 100 generations) is satisfied is determined. If it is satisfied, thegraph convolutional neural network provided in Step 3 is applied to thepopulation relationship network graph to learn the direct relationshipsbetween the nodes. An Adam optimizer with a learning rate of 0.01 is setfor use, and the adjusted and classified results of the nodes areobtained.

In Step 4.3, the GCN is used to classify the nodes in the population,and the preliminary Pareto frontier is supplemented by theclassification results to obtain a better Pareto frontier. The NSGA-IIalgorithm is then used to specifically adjust the nodes in the Paretofrontier to make the distribution of the Pareto frontier more uniform.The specific steps include the followings.

In Step 4.3.1, the GCN is used to classify nodes. The nodes areclassified according to the classification results. The number of thenodes in each classification will be supplemented, and the Paretofrontier will be better.

In Step 4.3.2, the number of the various node classifications in theabove-mentioned better Pareto frontier is calculated. Then, a portion ofthe nodes in the classifications having relatively more nodes aredeleted, and a portion of nodes are generated for the classificationshaving fewer nodes. The generation rules are as illustrated in FIG. 2 .

In Step 4.3.3, the NSGA-II algorithm is used to perform crossover andmutation operations again on the above-mentioned Pareto frontier toobtain a more uniform and accurate Pareto frontier.

In Step 4.3.4, whether the nodes satisfy the constraint conditions isdetermined, and if the nodes satisfy the constraint conditions, thenodes are retained.

In Step 5, the Pareto frontier is obtained when satisfying the endingconditions, that is, the result of the multi-objective optimization isachieved, and each objective efficiency and the set of reservoiroperation schemes are determined.

The method provided by the present disclosure is applied to themulti-objective optimal operation of the Xiaolangdi Reservoir during theflood season, in which the NSGA-II algorithm and the NSGADE algorithmare compared with each other with a small operation interval of fourhours and a total duration of 72 hours as an example. It can be seenfrom FIG. 5 that the Pareto solution set obtained by the method of thepresent disclosure is better than that of the NSGA-II algorithm and thatof the NSGADE algorithm. Moreover, by comparing the IGD values and HVvalues obtained by the three algorithms, it also shows that thealgorithm provided by the present disclosure has obvious advantages inthe convergence speed, wherein the IGD value is used to evaluate theconvergence and diversity of the algorithm by measuring theconformability degree between the true Pareto frontier and the Paretofrontier obtained by the algorithm, and the HV value is used to measurethe range covered by the Pareto solution set obtained by the algorithmin the objective space, which can evaluate the convergence and diversityat the same time. The less the IGD value, the better the convergence ofthe Pareto frontier obtained by the algorithm and the more uniform thedistribution. The greater the HV, the better the convergence of thePareto frontier obtained by the algorithm and the more uniform thedistribution. The detailed comparison is as follows.

Algorithm Comparison NSGADE NSGAII GCN_NSGA-II Algebra IGD HV IGD HV IGDHV 100 7.132 0.901 6.132 0.881 Training Training 200 2.511 0.903 3.5110.903 Training Training 300 1.111 0.909 3.111 0.905 1.961 0.906 4000.355 0.911 2.451 0.908 1.723 0.912 500 0.279 0.912 5.279 0.911 0.8390.918 600 0.272 0.913 1.872 0.915  0.831- 0.920 700 0.268 0.913 1.6680.920 0.826 0.922 800 0.262 0.915 1.262 0.923 0.823 0.924 900 0.2540.916 0.851 0.926 0.822 0.925 1000 0.251 0.918 0.554 0.928 0.821 0.926

To sum up, the multi-objective optimization problem of the reservoiroperation during flood seasons is modeled in the present disclosure, andthe influence of two objectives of the dam level and the maximumdischarge volume on the reservoir operation scheme is considered duringthe flood seasons. According to the specific factors such as thespecific reservoir and the surrounding environment, a specific model isfurther established. A set of operation schemes that satisfy all theobjectives can be obtained by using the algorithm provided in thepresent disclosure. A reasonable reservoir operation scheme cannot onlymaximize efficiencies for many parties, but also can ensure less damageto the ecological environment.

What is claimed is:
 1. A method for optimizing a reservoir operation formultiple objectives based on a graph convolutional neural network (GCN)and a Non-Dominated Sorting Genetic Algorithm (NSGA-II algorithm),wherein the method comprises following steps: Step 1, collectingrelevant data for reservoir flood-control operation and establishing amulti-objective optimization model for the reservoir operation; Step 2,obtaining an initial population of a multi-objective optimizationproblem for the reservoir operation by using the NSGA-II algorithm,grouping individuals in the population by an encoding operation andmarking the individuals with classifications, each of which is taken asa node in a GCN graphic structure, and mapping parent-childrelationships obtained by crossover and mutation operations as edgesbetween nodes in the GCN graphic structure, to obtain the GCN graphicstructure and a preliminary Pareto frontier; Step 3, grouping andlabeling abscissas of the preliminary Pareto frontier obtained in Step2, and then training a GCN model by using the grouping labels and theGCN graphic structure obtained in Step 2; Step 4, classifying the nodesin the GCN graphic structure by using the trained GCN model, and thenadjusting a uniformity of the Pareto frontier by using the NSGA-IIalgorithm until an algorithm iteration ends, to obtain a more uniformPareto frontier; and Step 5, outputting, according to the more uniformPareto frontier obtained in Step 4, a set of non-inferior schemes of themulti-objective optimization problem for the reservoir operation.
 2. Themethod for optimizing the reservoir operation for the multipleobjectives based on the graph convolutional neural network and theNSGA-II algorithm according to claim 1, wherein the objectivesconsidered in the multi-objective optimization model for the reservoiroperation in Step 1 comprise: firstly, minimizing an upstream waterlevel and ensuring that the reservoir maintains a low water level duringa flood season, thereby ensuring safety of a dam; and secondly,minimizing a maximum discharge volume in the reservoir, and storing asmuch floodwater as possible by the reservoir to ensure safety in adownstream to minimize an inundation loss.
 3. The method for optimizingthe reservoir operation for the multiple objectives based on the graphconvolutional neural network and the NSGA-II algorithm according toclaim 1, wherein Step 2 specifically comprises: Step 2.1, randomlyinitializing the population of the multi-objective optimization problemfor the reservoir operation, encoding the individuals in the populationaccording to a following encoding method, and taking encoded individualclassifications as the nodes in the GCN graphic structure; making,through the encoding method, a plurality of individuals in thepopulation belong to a same classification represented by a same node,to avoid a redundancy in the graphic structure caused by too manyindividuals in the population; the encoding method being that: adefinition domain of the maximum discharge flow Qmax is divided at anequal distance, each distance is ┌Q_(max)/N┐, where Qmax is the maximumdischarge volume, and N is a number of classifications, that is, anumber of nodes in the GCN graphic structure, and the individuals areencoded by using a method ┌Q/┌Q_(max)/N┐┐; the Pareto frontier isdivided at an equal distance by the abscissas, intervals of which aredefined as 0, 1, 2 . . . , wherein a node 0 is defined as an eliminationnode, and a length of a gene sequence in the population is determined bya number of variables; and Step 2.2, performing the crossover andmutation operations on the individuals in the population in Step 2.1 todetermine whether the constraint conditions are satisfied, and pointingcodes in the gene sequence of eliminated individuals that satisfy theconstraint conditions to the node 0; recording the individuals thatsatisfy the conditions, and defining the parent-child relationshipsgenerated by the crossover and mutation operations as the edges of thegraphic structure.
 4. The method for optimizing the reservoir operationfor the multiple objectives based on the graph convolutional neuralnetwork and the NSGA-II algorithm according to claim 1, wherein Step 3specifically comprises: Step 3.1, grouping and labeling the preliminaryPareto frontier obtained by the NSGA-II algorithm by the abscissas, thatis, dividing a value domain of an objective function at an equaldistance, to define digital labels; Step 3.2, setting input parameters,representing relationships between the individuals in the population byan adjacency matrix A∈R^(N×N) in the graph convolutional neural network,and initializing a characteristic matrix X∈R^(N×D); Step 3.3, taking aninput layer with N individuals as a first portion, that is, constitutingan N-layered input layer with N nodes in the graph, where thecharacteristic matrix X and the adjacency matrix A serve as inputs; Step3.4, taking a convolutional layer composed of two layers of graphconvolutions as a second portion, and transmitting characteristics of abase layer to a next layer by trigging information transmission of theedges between the two layers; and Step 3.5, taking an output layer as athird portion, and outputting, for the characteristic matrix X obtainedby calculating and transmitting of the two layers of convolutionallayers, in turn a classification probability of each of the nodesthrough an activation function.
 5. The method for optimizing thereservoir operation for the multiple objectives based on the graphconvolutional neural network and the NSGA-II algorithm according toclaim 1, wherein Step 4 specifically comprises: Step 4.1, obtaining thepreliminary Pareto frontier by the NSGA-II algorithm through selection,crossover and mutation operations, generating, during the process,relationships of a parent-child tree-shaped structure between theindividuals in the population of the multi-objective optimizationproblem for the reservoir operation, and converting the tree-shapedstructure into the GCN graphic structure; Step 4.2, determining whetherthe population iteration threshold is satisfied, and if satisfied,starting training the GCN, learning node characteristics in a populationevolution relationship graphic network, and making a node classificationresult correspond to a classification of the Pareto frontier; and Step4.3, classifying the nodes by using the GCN, and then adjusting theindividuals in the Pareto frontier through a loop iteration by using theNSGA-II algorithm, which specifically comprises following steps: Step4.3.1, classifying the nodes by using the GCN, and supplementing andimproving the preliminary Pareto frontier; Step 4.3.2, traversing thenodes with different classifications in the Pareto frontier, deletingredundant nodes with a same classification, and increasing population ofclassifications with a fewer number, to increase differences; Step4.3.3, performing the crossover and mutation operations on the nodeswith a good performance obtained through the GCN classification by usingthe NSGA-II algorithm to obtain new nodes; and Step 4.3.4, determiningwhether the nodes satisfy the constraint conditions, and retaining, ifsatisfied, the nodes.